Plano lens, rear-projection type projector screen employing the same, and rear-projection type video display apparatus

ABSTRACT

A piano lens according to the present invention includes a transparent base member disposed on a light emission side thereof or light incidence side thereof and a minute-transparent-ball disposing layer having at least minute transparent balls two-dimensionally in a single grain layer on the transparent base member so that the minute transparent balls disposed adjacent to each other should be disposed in contact with or close to each other, and a colored layer disposed so as to expose the minute transparent balls to outside on the light incidence side. The minute-transparent-ball disposing layer has an improved light transmission at a light emission side end portion of the minute transparent ball.

This application claims the benefit of division application Ser. No.08/864,824 filed May 29, 1997.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a plano lens, i.e., a piano lens foruse in a rear-projection type projector, a viewing-angle increasingplate of a liquid crystal display device, a plasma display device, anelectro-luminescent display device or the like, a light diffusion platefor diffusing a back light for a liquid crystal display, lights ofvarious illumination light sources or the like, and further to a screenfor a rear projection type projector.

The present invention relates to a rear-projection type video displayapparatus, i.e, a so-called rear-projection type projector.

2. Description of the Related Art

Recently, a projection-type display apparatus for emitting a luminousflux having a polarization characteristic, e.g., one employing a lightvalve such as a liquid crystal panel or the like has been developed. Theprojection type display apparatus employing a liquid crystal panel isarranged such that an image light spatially modulated by the liquidcrystal panel is enlarged by a projection lens and then projected on ascreen. The projection type display apparatus includes a frontprojection-type and a rear-projection type.

FIG. 1 is a perspective view showing a schematic arrangement of arear-projection type video display apparatus by which a user watches,from a front side of a screen 2, an image projected on the screen 2 froma rear side of the screen 2. The rear-projection type video displayapparatus has a video projector unit 1 for emitting projection videolight L, a transmission type screen 2, and a reflection mirror 3 forreflecting the projection video light L from the video projector unit 1to lead it to the transmission type screen 2.

This transmission type screen 2, i.e., a rear-projection type projectorscreen is usually formed of a Fresnel lens and a lenticular lens 5extended in the height direction of the screen 2.

In the rear-projection type video display apparatus having the abovearrangement, the Fresnel lens 4 converts the incident projection videolight L from the video projector unit 1 into substantially parallellight, and the lenticular lens 5 diffuses the substantially parallellight in the left and right direction (i.e., a width direction of thescreen 2).

Thus, the rear-projection type video display apparatus usually enlargesand projects the projection video light L from the video projector unit1. Specifically, a viewer watches an image obtained from the projectedlight transmitted through the transmission type screen 2.

However, it is frequently observed that the rear-projection type videodisplay apparatus is generally used in a bright room. In this case,external light such as room illumination light or the like is reflectedon a surface of the lenticular lens 5, and a viewer sees the reflectedlight together with the video light emitted from the screen 2, whichlowers the contrast of the image. In order to prevent the contrast ofthe image from being lowered, the rear-projection type video displayapparatus employs a smoke plate (not shown) in front of the lenticularlens 5 to absorb a part of the disturbance light, thereby suppressingthe lowering of the contrast.

When the smoke plate is provided as described above, the smoke platealso absorbs a part of the video light transmitted through the smokeplate similarly to the disturbance light, which lowers brightness of theimage. In order to increase the brightness, a light source having alarger consumed power is required. This becomes a bar to achieving moreefficient power consumption and requires a countermeasure forelimination of heat resulting from the increased consumed power, whichleads to a new problem of increasing the manufacturing costs.

A plano lens employing the lenticular lens, a transmission type screenemploying such plano lens, i.e., the rear-projection type projectorscreen, and a rear-projection type video apparatus employing such planolens and such rear-projection type projector screen have many problems.The problems are as follows.

(1) In the lenticular lens formed by extending a lens element in theupper and lower direction (vertical direction), light is diffused in thehorizontal direction, which allows a user to watch an image even from adiagonal direction. However, since light is seldom diffused in thevertical direction perpendicular to the horizontal direction, if theuser moves his viewpoint in the vertical direction, the user encountersthe disadvantages that a range within which the user can observe a sharpimage is extremely narrow.

Specifically, as shown in FIG. 3A, for example, in the rear-projectiontype video display apparatus employing the lenticular lens, as shown bya line a of FIG. 3A, an area within which of light vertically incidenton a plate surface of the lenticular lens is 50% or larger has a shapeof an elliptic cone which is flat in the vertical direction.Specifically, if an area within which at its center of light diffused inthe horizontal direction is 50% or larger of that obtained at its centeris an area having an angle of about 30°, then an area within which oflight diffused in the vertical direction is 50% or larger of thatobtained at its center is an area having an angle of about 20° as shownin FIG. 3C.

(2) Moreover, since the lenticular lens has a precise lens shape on thewhole surface, even if a slight defect lies in a part thereof, the wholeof the lens can not be used. Therefore, it is necessary to handle thescreen with a considerable case. Moreover, recent increase of a pictureprojected area requires more careful handling of the screen, whichinevitably leads to the increased costs.

(3) Since the screen formed by combining the Fresnel lens and thelenticular lens spreads the projected light mainly in the horizontaldirection, the screen provides a wide angle view in the horizontaldirection. On the other hand, the screen provides only a narrow angle ofview in the vertical direction. Therefore, some viewer recognizeunevenness of luminance distribution of an image and a partialunevenness thereof and sometimes recognize such uneven luminance as ahorizontal light band.

(4) When a black stripe is provided between lens elements of thelenticular lens, the black stripes cannot be formed at an intervalnarrower than a predetermined one in order to achieve a sufficienteffect of the lens, which lowers the contrast of the image and providesa low resolution.

(5) Moreover, since the projected light emitted from the video projectorunit 1 or the front-projection type video display apparatus or the likegenerally presents an illumination distribution in which illumination ata center portion corresponding to a picture angle is bright andillumination gradually becomes dark in the direction toward a peripheryside. Therefore, an illumination distribution of an picture presents asharp curve.

(6) In the screen formed by combining the above Fresnel lens and thelenticular lens, multiple reflection of light is produced between theFresnel lens and the lenticular lens, which shows a viewer observedimages which are overlapped one another.

(7) Moreover, it is sometimes observed that optical interference isproduced between the black stripe of the lenticular lens and theprojected image and hence a pattern resulting from the interference,i.e., a so-called moire occur in the observed image.

Use of the screen which diffuses light widely, i.e., the screen having aso-called wide diffusion provides only a low gain (luminance in adirection at a certain angle of emission/amount of incident light),i.e., a low luminance but can provide a flat gain curve having lessfluctuation with respect to an angle of view. On the other hand, thescreen having a strong directivity provides a high gain but the gain isdrastically lowered as the angle of view becomes larger. This drasticchange of the gain shows that movement of an observation position easilychanges brightness of a picture displayed on the screen when a userobserves a screen with the naked eyes.

As described in “Characteristics of rear projection screen andmeasurement method thereof” by Emori, “Optical technology contact” vol.11, No. 5 (1973 page 17 to page 23, especially page 18, since a humaneye has a logarithmic sensitivity with respect to luminance, even if thegain is fluctuated within a substantial range of a peak value which istwice as high as a lowest value, a user recognize only even brightness.

However, it is said that, if the gain is fluctuated beyond a range inwhich a peak value is three times as high as the lowest gain, then thereoccurs a so-called hot spot, i.e., hot band phenomenon that a portioncorresponding to a peak gain (which is usually located at the center ofthe screen) appears to be brighter.

According to the above letter, the most suitable screen has a peak gainof 3.5 and a gain obtained at a bend angle (angle of view) of 30° whichis higher than 25% of the peak gain.

A significance of measurement of screen performance with a gain at acertain bend angle will be described with reference to FIGS. 4 and 5.

It is assumed that a rear projector is attached to a screen having anaspect ratio of 16:9 and a user observes an image displayed on thescreen with the naked eyes being located at a position away from thescreen by a distance 3H which is three times as long as a height H ofthe displayed picture and being in front of a center position of thedisplay picture on the screen. The above distance 3H is considered as astandard observation distance for an NTSC television receiver and ahigh-definition television (HDTV) receiver.

In this case, when a viewer observes a wide-screen picture having anaspect ratio of 9:16 such as that of the HDTV, as shown in FIG. 4, bendangles in the vertical, horizontal, diagonal directions are 9.5°, 16.5°and 18.8° at most, respectively.

Further, when a plurality of viewers watch the screen, as shown in FIG.5, they watch the screen in front of the screen with being positioned inparallel to the screen, some viewer is positioned at a position whichcorresponds to a width-direction edge of the screen and is positionedaway from the screen by the distance 3H, and watches the screen with thenaked eyes being located at the same level as that of the center pointof the displayed picture. As a result, as shown in FIG. 5, bend anglesin the horizontal and diagonal directions are 30.7° and 31.6° at most,respectively.

Even in the above case, it is necessary to avoid a shading, i.e., aso-called uneven brightness on the screen. In general, even if theshading of 15% to 50% occurs, it is not so problematic when a viewerwatches the screen with the naked eyes. However, if the shading of 70%or larger occurs, it is not permissible. An area having the shading of50% or smaller caused when a viewer watches an image displayed on thescreen is called a favorable impression area. If this favorableimpression area is enlarged, then a screen area suitable for observationcan be enlarged.

In a practical projector, the shading is estimated in consideration ofan incident angle of a video light projected on a screen and evennessthereof. However, when the shading resulting only from a screen isestimated, it is possible to such shading in the form of values based ona relationship between a peak gain and a gain obtained at a certain bendangle.

However, recently, as a light projector unit employing an optical spacemodulation device (i.e., a light valve) such as a thin-film-transistorliquid crystal display or the like has been developed more, a projectorincreasingly obtains higher optical output year by year. Therefore,there is demanded a screen not only having a first effect of achieving ahigh peak gain but also having an effect in which some diffusion at thescreen enlarges an area suitable for observation.

SUMMARY OF THE INVENTION

It is an object of the present invention to solve the problems of aplano lens employing a lenticular lens and a rear-projection projectorscreen employing the piano lens.

It is another object of the present invention to secure both of a screenbrightness and some diffusion and to reduce manufacturing costs.

The above objects are achieved in accordance with the principles of thepresent invention in a piano lens having a light incident side and alight emission side and having a transparent base member disposed at oneof the light incident side and the light emission side and minutetransparent balls disposed two-dimensionally in a single ball layer onthe transparent layer, with the minute transparent balls beingsubstantially adjacent each other, and a color layer on the transparentlayer having the minute transparent balls respectively partially buriedtherein so that each of the minute transparent balls has an exposedsurface portion projecting from the color layer toward the lightincident side. Each of the minute transparent balls has an opticalcharacteristic, such as absorbence, spectral absorbence and refractiveindex, and this optical characteristic of some of the minute transparentballs differs in value from others of the minute transparent balls. Theminute transparent balls are respectively disposed in the single balllayer with a non-uniform distribution of the differing values of thisoptical characteristic.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a structural diagram showing a knowing rear-projection typevideo display apparatus;

FIG. 2 is a perspective view of a screen of the knowing rear-projectiontype video display apparatus shown in FIG. 1;

FIG. 3A is a diagram showing a distribution of illumination at a certainlevel or higher of light projected on a piano lens or a screen of theknowing rear-projection type video display apparatus shown in FIG. 1;

FIGS. 3B and 3C are diagrams used to explain the distribution shown inFIG. 3A;

FIG. 4 is a diagram used to explain a bend angle obtained when a userobserves a screen;

FIG. 5 is a diagram used to explain a bend angle obtained when a userobserves a screen;

FIG. 6 is a diagram showing an example of a rear-projection type videodisplay apparatus employing a screen according to the present invention;

FIG. 7 is a diagram showing another example of a rear-projection typevideo display apparatus employing a screen according to the presentinvention;

FIG. 8 is a cross-sectional view of a screen of the rear-projection typevideo display apparatus according to the present invention;

FIG. 9 is a schematic, cross-sectional view of a plano lens or a screenaccording to a first embodiment of the present invention;

FIG. 10 is a schematic, cross-sectional view of a plano lens or a screenaccording to a second embodiment of the present invention;

FIG. 11 is a schematic, cross-sectional view of a plano lens or a screenaccording to a third embodiment of the present invention;

FIG. 12 is a schematic, cross-sectional view of a plano lens or a screenaccording to a fourth embodiment of the present invention;

FIG. 13 is a schematic, cross-sectional view of a piano lens or a screenaccording to a fifth embodiment of the present invention;

FIG. 14 is a schematic, cross-sectional view of a plano lens or a screenaccording to a sixth embodiment of the present invention;

FIG. 15 is a schematic, cross-sectional view of a plano lens or a screenaccording to a seventh embodiment of the present invention;

FIG. 16 is a schematic, cross-sectional view of a piano lens or a screenaccording to an eighth embodiment of the present invention;

FIG. 17 is a schematic, cross-sectional view of a piano lens or a screenaccording to a ninth embodiment of the present invention;

FIG. 18 is a schematic, cross-sectional view of a plano lens or a screenaccording to a tenth embodiment of the present invention;

FIG. 19 is a schematic, cross-sectional view of a plano lens or a screenaccording to an eleventh embodiment of the present invention;

FIG. 20 is a schematic, cross-sectional view of a plano lens or a screenaccording to a twelfth embodiment of the present invention;

FIG. 21 is a schematic, cross-sectional view of a plano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 22 is a schematic, cross-sectional view of a piano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 23 is a schematic, cross-sectional view of a piano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 24 is a schematic, cross-sectional view of a piano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 25 is a schematic, cross-sectional view of a piano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 26 is a schematic, cross-sectional view of a piano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 27 is a schematic, cross-sectional view of a piano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 28 is a schematic, (cross-sectional view of a piano lens or ascreen according to the present invention with an anti-reflection layer;

FIG. 29 is a schematic, cross-sectional view of a plano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 30 is a schematic, cross-sectional view of a plano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 31 is a schematic, cross-sectional view of a piano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 32 is a schematic, cross-sectional view of a plano lens or a screenaccording to the present invention with an anti-reflection layer;

FIG. 33 is a graph used to explain dependence of a refractive index of aminute transparent ball on an angle of view;

FIGS. 34A, 34B and 34C are distributions of illumination, gain andbrightness, respectively;

FIG. 35 is a diagram showing distribution of a refractive index of theplano lens or the screen according to the present invention;

FIG. 36 is a diagram showing distribution of a refractive index of theplano lens or the screen according to the present invention;

FIG. 37A is a diagram showing a distribution of illumination at acertain level or higher of light projected on a plano lens or a screenof the rear-projection type video display apparatus according to thepresent invention;

FIGS. 37B and 37C are diagrams used to explain the distributionaccording to the present invention;

FIGS. 38A to 38C are graphs used to explain distributions ofilluminance, gain and screen luminance of the plano lens or the screenaccording to the present invention;

FIG. 39 is a diagram used to explain measurement of luminance of thescreen according to the present invention;

FIG. 40 is a diagram showing an arrangement of the screen according tothe present invention;

FIG. 41 is a graph showing luminance curves obtained when a minutetransparent ball of one kind is used;

FIG. 42 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive indexes of 1.9 and 1.6are used;

FIG. 43 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive indexes of 1.9 and 1.6are used;

FIG. 44 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive indexes of 1.9 and 1.6are used;

FIG. 45 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive indexes of 1.9 and 1.6are used;

FIG. 46 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 2.1 and 1.9are used;

FIG. 47 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 2.1 and 1.8are used;

FIG. 48 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive indexes of 2.1 and 1.7are used;

FIG. 49 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 2.1 and 1.6are used;

FIG. 50 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 2.1 and 1.5are used;

FIG. 51 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 2.1 and 1.8are used;

FIG. 52 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 1.9 and 1.7are used;

FIG. 53 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 1.9 and 1.6are used;

FIG. 54 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 1.9 and 1.5are used;

FIG. 55 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 1.9 and 1.7are used;

FIG. 56 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 1.8 and 1.6are used;

FIG. 57 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 1.8 and 1.5are used;

FIG. 58 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive index of 1.7 and 1.6are used;

FIG. 59 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive indexes of 1.7 and 1.5are used;

FIG. 60 is a graph showing luminance curves obtained when the minutetransparent balls of two kinds having refractive indexes of 1.6 and 1.5are used; and

FIG. 61 is a graph showing luminance curves obtained when the minutetransparent balls of three kinds having refractive indexes of 1.7, 1.8and 1.9 are used.

FIG. 62 shows an embodiment of a minute-transparent-ball having convexprojections; and

FIG. 63 shows an embodiment of a minute-glass-ball having concavedepressions.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Initially, piano lenses and rear-projection type projector screensemploying the plano lenses according to embodiments of the presentinvention will be described.

Each piano lens according to the embodiments of the present inventionhas, as shown in FIGS. 9 to 32 which are cross-sectional views thereof,a transparent base member 11 provided on at least one of a lightemission side or a light incidence side, and a minute-transparent-balldisposing layer 14 having minute transparent balls 12 disposedtwo-dimensionally on the transparent base member 11 so as to form asingle grain layer and to be in contact with or close to one another,and having a colored layer 13 used for exposing a part of each of theminute transparent balls 12 on the light incidence side. Theminute-transparent-ball disposing layer 14 is arranged so as to enhancetransmittance of each minute transparent ball 12 at the light emissionside end portion. As will be described later on, since each minutetransparent ball 12 converges the incident light, it is sufficient forthe minute transparent ball 12 to have a small area where light isemitted, and hence the minute-transparent-ball disposing layer 14 mayhave a small area having high transmittance.

Each of rear-projection type video display apparatus according to firstand second embodiment of the present invention will be described.

The rear-projection type video display apparatus has, as shown in FIGS.6 and 7 which are schematic diagrams showing examples of an arrangementthereof, a video projector unit 1 and a transmission type screen 10S.

The rear-projection type video display apparatus shown in FIG. 6 has aprojecting apparatus 60 having the video projector unit 1 on a back sideof the transmission type screen 10S. Projected light emitted from theprojecting apparatus 60 is projected on the screen 10S, and a viewerwatches an image obtained from the projected light transmitted throughthe screen 10S and diffused thereby in the vertical and horizontaldirections, from the front of the screen 10S.

The rear-projection type video display apparatus shown in FIG. 7 has thetransmission type screen 10S at the front face of a case body 61. Animage obtained from light from the video projector unit 1 provided inthe case body 61 is reflected by a reflection mirror 3, and a viewerwatches an image obtained from the projected light transmitted throughthe screen 10S and diffused thereby in the vertical and horizontaldirections, from the front of the screen 10S.

The transmission type screen 10S employed by these rear-projection typevideo display apparatus shown in FIGS. 6 and 7 employs a plano lenshaving a special arrangement described later on. Specifically, as shownin FIG. 8 which is a schematic, cross-sectional view of the plano lens,the plano lens has transparent base members 11 and 41 are disposed onboth of the light emission side and the light incidence side of thescreen 10S, and the minute transparent ball disposing layer 14 disposedbetween the transparent base members 11 and 41. The minute transparentball disposing layer 14 has the minute transparent balls 12 disposedtwo-dimensionally on the transparent base member 11 so as to form asingle grain layer and to be in contact with or close to one another.The minute-transparent-ball disposing layer 14 has at least the coloredlayer 13 used for exposing a part of each of the minute transparentballs 12 to the outside on the light incidence side. In FIG. 8,anti-reflection layers 28 are formed on both of outer aside surfaces ofthe screen 10S.

The transmission type screen 10S forming the plano lens, therear-projection type projector screen, and the rear-projection typevideo display apparatus according to the present invention will bedescribed. Hereinafter, the transmission type screens forming the planolens, the rear-projection type projector screen, and the rear-projectiontype video display apparatus according to the embodiments are allreferred to as the plano lens according to the present invention.

A plano lens 10 according to a first embodiment of the present inventionshown in FIG. 9 has a transparent base member 11 formed of a glasssubstrate having rigidity or a plastic substrate or a flexible substrateand disposed on the light emission side of the lens 10. Specifically, inthis case, a minute-transparent-ball disposing layer 14 is formed on thelight incidence side of the transparent base member 11. In the firstembodiment, the minute-transparent-ball disposing layer 14 is formedsuch that minute transparent balls 12 are disposed densely in a singlegrain layer with the adjacent minute transparent balls 12 beingsufficiently close to each other or in contact with each other and thateach of the minute transparent balls 12 is partially buried in a coloredlayer 13 having adhesion or cohesion and fixed therein. Specifically,each of the minute transparent balls 12 is disposed to have a lightincident surface portion corresponding to 30% or larger of a diameter ofthe minute transparent ball 12, this surface portion being projectingthereof from the colored layer 13, and each ball 12 having a lightemission portion in the colored layer 13 buried. Each of the minutetransparent balls 12 is in contact with the transparent base member 11directly or through a sufficiently thin portion of the color layer 13 atthe light emission end side of the minute transparent ball 12.Therefore, at the light emission end side, light transmittance isincreased with almost no light being absorbed by the colored layer 13.Thus, of an amount of light emitted from the minute transparent ball 12,the light amount absorbed by the colored layer 13 is reduced. An areawhere the amount of light absorbed by the colored layer 13 is reducedcan be set as a minute area on the light emission end side of the minutetransparent ball 12.

In the plano lens 10 according to the first embodiment, when incidentlight Li, in the form of parallel light representing a projected imageor the like, is incident on the exposed surface portions of the minutetransparent balls 12 of the minute-transparent-ball disposing layer 14from the opposite side thereof with respect to the transparent basemember 11, the incident light Li is converged and then diverged due to alens effect by the minute transparent ball 12 and hence emitted light Lois diffused. Thus, a diffusion plano lens or view angle enlarging pianolens is formed.

As described above, the area where the amount of light absorbed by thecolored layer 13 is reduced is formed at the emission end of each of theminute transparent balls 12, thereby the emission light being allowed tobe efficiently emitted in the front direction of the plano lens 10.Since light is converged by each of the minute transparent balls 12 andthen emitted, it is possible that the above area of each of the minutetransparent balls 12 has a minute area. Since the colored layer 13,i.e., a light absorbing layer lies around the above area, external lightLd is effectively absorbed by the colored layer 13 and hence can beeffectively prevented from travelling in undesired directions.Therefore, it is possible to effectively prevent the contrast of apicture displayed on a screen from being lowered due to the externallight Ld.

Plano lenses 10 according to the second to eighth embodiments willhereinafter be described with reference to FIGS. 10 to 16. In FIGS. 10to 16, like parts corresponding to those shown in FIG. 9 are marked withthe same reference numerals and need not to be described in detail.

FIG. 10 is a diagram showing a plano lens 10 according to a secondembodiment of the present invention. In the second embodiment, the planolens 10 has an arrangement similar to that described with reference toFIG. 9. However, in the second embodiment, as shown in FIG. 10, aminute-transparent-ball disposing layer 14 has a bi-layer structureformed of a colored layer 13 and a transparent layer each of which hasadhesion or cohesion. In this case, since the transparent layer 15 isdisposed on the light emission end side thereof, light transmittance atthe light emission end side is increased and hence it is possible toobtain a larger amount of light emitted from the minute transparentballs 12. In this embodiment, since the minute transparent balls 12 areburied in both of the colored layer 13 and the transparent layer 15, theminute transparent balls 12 can be held more tightly.

Plano lenses 10 according to third and fourth embodiments shown in FIGS.11 and 12 respectively have the same arrangements as those according tothe first and second embodiments shown in FIGS. 9 and 10 and arerespectively arranged such that each has a transparent protective layer25 having adhesion or cohesion relative to the minute transparent balldisposing layer 14 is disposed on the opposite side of the minutetransparent ball disposing layer 14 relative to the transparent basemember 11. The minute transparent balls 12 thus are protected on theirsides opposite the sides in contact with the transparent base member 11.

Plano lenses 10 according to fifth and sixth embodiments shown in FIGS.13 and 14 respectively have arrangements similar to those according tothe first and second embodiments shown in FIGS. 9 and 10 except that ineach the transparent base member 11 is disposed on the light incidencesides of the minute transparent ball disposing layer 14. The minutetransparent ball disposing layer 14 is bonded to the transparent basemember 11 by a transparent layer 26 having adhesion or cohesion.

Plano lenses 10 according to seventh and eighth embodiments shown inFIGS. 15 and 16 respectively have arrangements similar to thoseaccording to the first or fifth embodiment shown in FIG. 9 or 13 and thesecond or sixth embodiment shown in FIG. 10 or 14 except that in eachthe transparent base member 11 and the protective transparent basemember 41 are disposed so as to sandwich the minute-transparent-balldisposing layers 14. This arrangement can maintain strength of the planolens 10 and can prevent the minute transparent balls 12 in theminute-transparent-ball disposing layer 14 and the colored layer 13 frombeing damaged and soiled. The protective transparent base member 41 maybe made of the same material as that used for the transparent basemember 11. Alternatively, one of the transparent base member 11 and theprotective transparent base member 41 may be formed of a rigidsubstrate, the other thereof being formed of a flexible base member.

While the plano lens 10 according to the present invention can form therear-projection type projector screen by itself, as shown in FIGS. 17 to20, the rear-projection type projector screen 10S can be formed byintegrally bonding the plano lens 10 with a Fresnel lens 27 used formaking projected video light incident on the piano lens 10 as parallellight.

FIGS. 17 to 20 are diagrams showing rear-projection type projectorscreens 10S in each of which a Fresnel lens 27 is formed on atransparent base member 31. In FIGS. 17 to 20, like parts correspondingto those shown in FIGS. 9 to 16 are marked with the same referencenumerals and need not to be described in detail.

In the rear-projection type projector screen 10S according to a ninthembodiment shown in FIG. 17, a Fresnel lens 27 is bonded by atransparent layer 26 having adhesion or cohesion to the piano lens 10according to the first embodiment shown in FIG. 9 (i.e., to the lightincidence side of the minute transparent ball 12 shown in FIG. 9).

In the rear-projection type projector screen 10S according to a tenthembodiment shown in FIG. 18, a Fresnel lens 27 is bonded by atransparent layer 26 having adhesion or cohesion to the piano lens 10according to the second embodiment shown in FIG. 10 (i.e., to the lightincidence side of the minute transparent ball 12 shown in FIG. 10).

In the rear-projection type projector screen 10S according to aneleventh embodiment shown in FIG. 19, in stead of the transparent basemember 11 shown in FIG. 13, a Fresnel lens 27 is bonded by a transparentlayer 26 having adhesion or cohesion to the plano lens 10 according tothe fifth embodiment shown in FIG. 13 (i.e., to the light incidence sideof the minute transparent ball 12 shown in FIG. 13).

In the rear-projection type projector screen 10S according to a twelfthembodiment shown in FIG. 20, in stead of the transparent base member 11shown in FIG. 14, a Fresnel lens 27 is bonded by a transparent layer 26having adhesion or cohesion to the piano lens 10 according to the sixthembodiment shown in FIG. 14 (i.e., to the light incidence side of theminute transparent ball 12 shown in FIG. 14).

As described above, when the Fresnel lens 27 is bonded instead of thetransparent member 11 in the arrangement according to the eleventh andtwelfth embodiments, it is possible to simplify the arrangement of thescreen 10S.

In each of the arrangements according to the first to twelfthembodiments shown in FIGS. 9 to 20, as shown in FIGS. 21 to 32, ananti-reflection layer 28 is deposited on both of outermost surfaces onthe light incidence side and the light emission side of each of thepiano lenses 10 and the screens 10S according to the first to twelfthembodiments. Such arrangement can allow the incident light to beeffectively made incident on the plano lens 10 or the screen 10S andalso allows the emission light to be effectively emitted therefrom. InFIGS. 21 to 32, like parts corresponding to those shown in FIGS. 9 to 20are marked with the same reference numerals and need not to be describedin detail. While in each of the arrangements shown in FIGS. 21 to 32 theanti-reflection layer 28 is deposited on both of the outermost surfaceson the light incidence side and the light emission side of the planolens 10 or the screen 10S, the anti-reflection layer 28 may be depositedon only one surface thereof. Glare preventing layers (not shown) can befurther deposited on each of the plane lenses 10 and the screens 10Sshown in FIGS. 21 to 32. Moreover, a protective transparent layer suchas a scratch preventing layer for protecting the transparent basemember, the minute-transparent-ball disposing layer 14 or the likedisposed on the outermost side can be formed instead of or on theanti-reflection layers 28 or instead of one of the anti-reflectionlayers 28. When the anti-reflection layers 28 or the protectivetransparent layers such as the scratch preventing layer are formed asdescribed above, it is possible to increase the light transmittance ofthe plano lens 10 or the screen 10S, to reduce reflectivity thereof, andto avoid damage, which improves an optical performance of the plano lens10 and the screen 10S.

In the plano lens 10 and the screen 10S according to the presentinvention, each of the transparent base members 11, 41 and 31 can beformed of a transparent or semitransparent and comparatively thicksubstrate or a comparatively thin flexible she et each of which haslight transmission capable of providing an action as a lens.

Each of the transparent base members 11, 41 and 31 is formed of somesuitable material such as, for example, glass, acrylic resin,polycarbonate resin, polyolefin resin, vinyl chloride resin, polystyreneresin, polyethylene resin, epoxy resin, polyarylate resin, polyethersulfone resin, silicone resin, poly(ethhylene terephthalate) resin orthe like.

Each minute transparent ball 12 can be formed of a glass bead or aplastic bead made of acyrlic resin, polystyrene resin or the like. Theminute transparent ball 12 is formed of a material having a refractiveindex of 1.4 or larger and having a refractive index larger than that ofa material in contact therewith, e.g., the protective transparent layer25 or the transparent layer 26 used for bonding, thereby the incidentlight being effectively introduced into the minute transparent ball 12for providing an action as a lens.

A diameter of the minute transparent ball 12 is set equal to or smallerthan 100 μm, e.g, about 50 μm. The size of the minute transparent balls12 were larger, when the rear-projection type projector screen isnormally used, a viewer can more easily recognize gaps between theminute transparent balls 12 with the naked eyes, which results in alowered resolution and a deteriorated picture quality of a projectedpicture. If the diameter of the minute transparent ball 12 is set equalto or smaller than 100 μm, the resolution is 5 lines/mm, and if thediameter of the minute transparent ball 12 is set equal to or smallerthan 50 μm, the resolution is 10 lines/mm. On the other hand, aresolution of the conventional lenticular lens is 1 line/mm.

While a lower limit of the size of the minute transparent ball 12 is notset, if the size of the minute transparent ball 12 is too small, then itbecomes difficult to dispose the minute transparent balls 12 in a singlegrain layer and it becomes difficult to form the bonding layer and tomake a thickness of the bonding layer uniform.

Fluctuation of the sizes of the minute transparent balls 12 are setwithin the range of 10% or less of a mean diameter. The reason for thisis that it is confirmed if the fluctuation of the diameters of theminute transparent balls 12 is increased, then a process of denselyfilling the minute transparent balls 12 in the minute-transparent-balldisposing layer 14 cannot be carried out satisfactorily and uniformly.

The refractive index of the minute transparent ball 12 is set largerthan those of the surrounding portions and particularly the surroundingportions on the light incidence end side. In order to obtain asufficient effect of a converging lens, the refractive index of theminute transparent ball 12 is set equal to or larger than 1.4.

As will be described later on, a light converging effect is determinedin response to a value of the refractive index of the surroundingportions on the light incidence end side of the minute transparent balland a value of the refractive index of the minute transparent ball, andhence a diffusion angle on the light emission side of the minutetransparent ball is determined. Therefore, since diffusion angles of theplano lens and the screen according to the present invention aredetermined in accordance with the law of refraction in optics (i.e.,Snell's law of refraction), it is possible to obtain a desired diffusionangle by selecting refractive indexes of the respective parts andmembers of the piano lens or the screen.

The surface of the minute transparent ball 12 may be subjected both ofor either of an anti-reflection processing and a water-repellencyprocessing.

While the surface of the minute transparent ball 12 can be set as anoptically smooth surface, the surface of the minute transparent ball 12can be set as a surface having minute concaves and convexes to an extentthat the minute transparent balls 12 can be filled densely, thereby aneffect of scattering being controlled and adjusted. Alternatively, if itis desired to avoid unnecessary reflection and scattering at the surfaceof the minute transparent ball 12, the surface of the minute transparentball 12 can be subjected to the anti-reflection processing or can besubjected to the water-repellency processing in the manufacturingprocesses if necessary. For example, if the water-soluble colored layer13 is formed, then the surface of the minute transparent ball 12 can bepreviously subjected to the water-repellency processing in order toprevent the colored layer from covering the light incidence end side ofthe minute transparent ball 12.

The colored layer 13 in the minute-transparent-ball disposing layer 14can be formed of a block pigment such as carbon or the like, a blockpigment such as a so-called toner obtained by mixing a binder withcarbon or the like and a block dye of aniline system or the like, can beformed by dispersing a black pigment in a transparent resin such asacrylic resin, polycarbonate resin, polyolefin resin, vinyl chlorideresin, polystyrene resin, polyethylene resin, epoxy resin, polyarylateresin, polyether sulfone resin, silicone resin, poly(ethhyleneterephthalate) resin or the like, can be formed of a layer made of ablack material dyed with a black dye. The colored layer 13 can be formedof a material layer having functions such as adhesion, cohesion or thelike in necessity in fabrication is caused.

The colored layer 13 is not limited to the black layer and may be alayer having spectral distribution of red, green, blue or the like. Thecolored layer can be formed of a material obtained by mixing a pluralityof pigments or dyes having different color distributions.

In the minute-transparent-ball disposing layer 14, the minutetransparent ball 12 is projected i.e., exposed from the colored layer 13on the light incidence side by an amount corresponding to 30% or longerof the diameter of the minute transparent ball 12 and more preferably50% or longer thereof. If the projected amount is smaller than 30% ofthe diameter, then an amount of incident light entering the minutetransparent ball 12 is reduced, which may prevent the effective minutetransparent ball 12 from presenting an effect of diffusing the incidentlight. If on the other hand the exposed amount of the minute transparentball 12 relative to the colored layer 13 is increased, then the amountof the light incident on the minute transparent ball 12 is increased,which increases the luminance. However, an upper limit of the exposedamount is subject to the thickness of the colored layer 13.Specifically, the thickness of the colored layer 13 corresponds to 70%of the diameter of the minute transparent ball 12, while a lower limitof the thickness of the colored layer 13 is determined depending uponabsorbance or spectral absorbance of the colored layer 13. Specifically,if the absorbance or the spectral absorbance is small and the thicknessof the colored layer 13 is thin in consideration of the incident light,then the incident light is transmitted through the colored layer 13,which increases an amount of light which is not diffused by the minutetransparent ball 12. As a result, the inherent characteristics of thepiano lens is deteriorated, and an amount of absorbed external lightfrom the emission side are lowered, which lowers the contrast of theimage.

The above protective transparent layer, e.g., the transparent layer 25,the transparent layer formed at the outermost side, the transparentlayer 26 and further the transparent layer 15 of the minute transparentball disposing layer 14 can be formed of transparent resin such asacrylic resin, polycarbonate resin, polyolefin resin, vinyl chlorideresin, polystyrene resin, polyethylene resin, epoxy resin, polyarylateresin, polyether sulfone resin, silicone resin, poly(ethhyleneterephthalate) resin or the like. Even if the above protectivetransparent layers are employed in the same plano lens, it is notnecessary to form the protective transparent layers of the samematerial, and proper materials can be selected for the respectiveprotective transparent layers depending upon the method of manufacturingthe piano lens. For example, the transparent layer 15 of theminute-transparent-ball disposing layer 14 may be formed of a materialhaving cohesion for holding the light emission side end portion of theminute-transparent-ball disposing layer 14 with the light emission sideend portion being buried therein, and the transparent layer 26 may beformed of a material having adhesion or cohesion.

While each of the protective transparent layer 25, transparent layer 26,the transparent layer 15 of the minute-transparent-ball disposing layer14 and so on can be formed of a single layer, each of them may be formedby laminating a plurality of layers made of different materials selectedfrom the above transparent materials and so on.

Other than acrylic resin, polycarbonate resin, polyolefin resin, vinylchloride resin, polystyrene resin, polyethylene resin, epoxy resin,polyarylate resin, polyether sulfone resin, silicone resin,poly(ethhylene terephthalate) resin or the like, the anti-reflectionlayer 28 and the protective transparent layer such as the scratchprevention layer or the like can by formed of tetraethyl orthosilicateby chemical vapor deposition or formed by depositing SiO₂ or metal thinfilm by vacuum evaporation, sputtering, sol-gel process or the like.

The above respective transparent layers, the colored layer and so on canbe coated by knife coating, e.g., roll coating, gravure coating, kisscoating, spray coating, blade coating rod coating or the like.

As shown in FIG. 6, the projector apparatus 60 is disposed at the backof the screen employing the plano lens 10 according to the presentinvention, e.g., one of the screens 10S shown in FIGS. 14 to 17 andFIGS. 26 to 29, the projector apparatus 60 projects a projected pictureon the screen 10S. The viewer watches a transmitted picture diffused inthe vertical and horizontal directions by the screen 10S from the frontof the screen 10S.

As shown in FIG. 7, the screen 10S is disposed at the front side of thecase body 61, and the light from the video projector unit 1 disposed inthe case body 61 is reflected by the reflection mirror 3, thus a viewerwatching the transmission image diffused by the screen 10S in thevertical and horizontal directions from the front of the screen 10S.

In the plano lens 10 and the screen 10S employing the piano lens 10according to the present invention, the minute transparent balls 12 ofthe minute-transparent-ball disposing layer 14 can be formed of minutetransparent balls of two kinds or more having different refractiveindexes.

Specifically, in the above arrangements, as the minute transparent ball12 of the minute-transparent-ball disposing layer 14 has a largerrefractive index, its action as the lens, i.e., the convergence effectis improved and hence the diffusion angle becomes larger. In FIG. 33,curves 27A, 27B and 27C represent dependence of gains upon an angle viewobtained when the angle is an angle of view (angle relative to anincident angle) θ on the emission side obtained when light is madevertically incident on a transparent substrate 51 in which the minutetransparent balls 12 are disposed in a single grain layer and therefractive index n of the minute transparent ball 12 is set to n=1.7,n=1.8 and n=1.9. Study of FIG. 33 reveals that as a value of θ isincreased, each of the gains is lowered, but when an picture displayedon a screen is observed from a range of a small value of θ, i.e., from asubstantial just front position, as the refractive index is larger, thegain is smaller.

The present invention is made in consideration of this phenomenon.According to the present invention, it is an object of the presentinvention that one lens or one screen is formed by mixing the minutetransparent balls of two kinds or larger having different refractiveindexes or by disposing them in a predetermined distribution and hencethe lens or the screen is arranged such that the refractive index ischanged stepwise or gradually from the center portion to the peripheryportion, thereby desired brightness being obtained in each of theportions of one lens or one screen.

Specifically, illumination light from a normal light source or lightrepresenting a picture in a predetermined picture angle from the videoprojector unit, as shown in FIG. 34A which is a graph showing anillumination distribution thereof, is the largest at the center of thepicture and becomes smaller as the position is away from the center.Therefore, when the illumination light or the light representing apicture is made incident on the plano lens or the screen, brightness ofthe screen on the emission side is large at the center and becomesdarker in the direction toward the periphery.

As shown in FIG. 35, in the piano lens 10 or the screen 10S according tothe present invention, the minute transparent balls 12 having arefractive index of n=1.9 are disposed in a region A at its center, theminute transparent balls 12 having a refractive index of n=1.8 aredisposed in a region B located at its outer side of the region A, andthe minute transparent balls 12 having a refractive index of n=1.7 aredisposed in a region C at its outermost periphery.

Alternatively, the piano lens 10 or the screen 10S is arranged such thatthe refractive index is gradually changed from n=1.9 to n=1.7 from thecenter to the outermost periphery. In this case, such arrangement isachieved by concentrically disposing the minute transparent balls 12 ofplural kinds having different refractive indexes so as to successivelychange the refractive index from n=1.9 to n=1.7, and also achieved bychanging a mixing ratio of the minute transparent balls having differentrefractive indexes so that the refractive index should be successivelychanged from n=1.9 to n=1.7 from the center to the outermost periphery.

When the refractive index of the plano lens 10 and the screen 10S ischanged from the center to the periphery as described above, asschematically shown in FIGS. 37A to 37C, a diffusion-angle regionindicative of 50% of the center luminance in the vertical and horizontaldirections is large at the center of the screen and small at theperiphery thereof as indicated by cones a and c shown in FIG. 37A. Forexample, the region with the refractive index of n=1.9 has horizontaland vertical enlargement angles α≧45° as shown in FIG. 37B, and theregion with the refractive index of n=1.7 has horizontal and verticalenlargement angles a of about 15° as shown in FIG. 37C.

Specifically, the gain distribution of the plano lens 10 or the screen10S is small at the center thereof and large at the periphery thereof asshown in FIG. 34B, which can compensate the illumination distributionshown in FIG. 34A to thereby flattening the brightness of lighttransmitted through the plano lens 10 or the screen 10S as shown in FIG.34C.

In this case, when the illumination distribution is the largest at thecenter of the screen and becomes smaller in the direction toward theperiphery, the brightness is made even. Contrary, as shown in FIG. 38Awhich is a graph showing illumination, when illumination of the lightirradiated on the plano lens 10 or the screen 10S is the smallest at thecenter thereof and becomes larger in the direction toward the peripherythereof, the brightness can be Lade even by the same method as describedabove. Specifically, contrary to the above method, the plano lens 10 orthe screen 10S is arranged such that the refractive index n of theminute transparent balls 12 is set small at the center thereof andlarger in the direction toward the peripheral portion. Then, as shown inFIG. 38B, the gain is set the largest at the center and becomes smallerin the direction toward the periphery. Thus, as shown in FIG. 38C, it ispossible to make the brightness of the light transmitted through theplano lens 10 or the screen 10S flat, i.e., even.

While in this embodiment the brightness of the light transmitted throughthe plano lens 10 or the screen 10S is made even (flat) at each of thepositions thereof, the present invention is not limited thereto and therefractive index of the minute transparent balls 12 can be changed inorder to positively change the brightness distribution to a desireddistribution.

As described above, when the minute transparent balls of two kinds ormore having different refractive indexes are employed in one lens or onescreen, the refractive indexes of the minute transparent balls 12 havingdifferent refractive indexes and the mixing ratio thereof are set todesired values, it is possible to realize the rear-projection type videodisplay apparatus employing the plano lens and the rear-projection typeprojector screen having the peak gain of 2.4 or greater and a gainobtained at the bend angle of 30° which is larger than ⅓ or greater ofthe peak gain.

FIG. 39 is a diagram showing a method of measuring luminance obtainedwhen the bend angle with respect to the screen forming therear-projection type video display apparatus according to the presentinvention is changed.

Specifically, as shown in FIG. 39, light emitted from a light source 101is made incident of a rear surface of a screen, and luminance of lightemitted from a portion in the vicinity of the front center of the screenis measured by a luminancemeter located away from the screen by apredetermined distance with respect to every 5° of the bend angle.

As shown in FIG. 40, the screen shown in FIG. 39 has structure formed ofsix layers of an incident side transparent substrate 103, an incidentside transparent adhesion layer 104, minute transparent balls 12, alight absorbing layer 105, an emission side transparent adhesion layer106, and an emission side transparent substrate 107.

The incident side transparent substrate 103 can be formed of acrlicresin (polymethyl methacrylate). The incident side transparent adhesionlayer 104 can be formed of an adhesive of acrylic system. The minutetransparent ball 12 can be formed of glass. The light absorbing layer105 can be formed of a toner (carbon powder). The emission sidetransparent adhesion layer 106 can be formed of an acrylic adhesive. Theemission side transparent substrate 107 can be formed of acrylic resin(polymethyl methacrylate).

When the luminance of the screen was measured, a refractive index n ofthe minute transparent ball 12 of the layers forming the screen wasoptionally selected from values of 1.5, 1.6, 1.7, 1.8, 1.9 and 2.1, andrefractive indexes of other layers are fixed on optional values. Theluminance was measured on the assumption that parallel rays of lightswere made incident on the screen from the light incidence side. Anamount of light, which is refracted and absorbed in each of the layers,emitted at the emission side of the screen is measured or calculated bysimulation using a ray tracing method with respect to a bend angle.

FIG. 41 is graph showing measurement of luminance obtained when theminute transparent ball 12 of one kind was employed and the refractiveindex n of the minute transparent ball was changed. In FIG. 41, curves41 a, 41 b, 41 c, 41 d, 41 e and 41 f are luminance curves respectivelyobtained when n=1.5, n=1.6, n=1.7, n=1.8, n=1.9 and n=2.1.

FIG. 42 is a graph showing a result of the simulation. In FIG. 42,curves 42 a, 42 b, 42 c, 42 d, 42 e and 42 f are luminance curvesrespectively obtained when n=1.5, n=1.6, n=1.7, n=1.8, n=1.9 and n=2.1.

Study of FIGS. 41 and 42 reveals that the gain curves shown in FIGS. 41and 42 coincides with each other and hence this simulation result shownin FIG. 42 is equal to the measurement shown in FIG. 41.

Table 1 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent ball 12 of one kind wasemployed. In this case, when a value of the peak gain is equal to orlarger than 2.4, the result is evaluated with an open circle, and whenthe value is smaller than 2.4, the result is evaluated with a cross.When a value of the gain obtained at a bend angle of 30° is equal to orlarger than ⅓ of larger, i.e., 33% or larger of the peak gain, theresult is evaluated with an open circle, and when the value is smallerthan 33%, the result is evaluated with a cross.

TABLE 1 screen arrangement gain shading gain 300 one kind peak 30° 20°2.4 or more 33% or more n = 2.1 1.192 64% 18% X ◯ n = 1.9 1.952 49% 30%X ◯ n = 1.8 3.363 31% 48% ◯ X n = 1.7 6.637 13% 70% ◯ X n = 1.6 20.622 2% 93% ◯ X n = 1.5 396.42  0% 100%  ◯ X

Study of Table 1 reveals that the screen employing the minutetransparent ball 12 of one kind could not satisfy the conditions of thepeak gain of 2.4 or more and the gain obtained at the bend angle of 30°being equal to or larger than 33%.

FIG. 43 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n were employed with being mixed in a ratio of 8:2. In FIG. 43,curves 43 a, 43 b, 43 c, 43 d are luminance curves respectively obtainedwhen the minute transparent balls 12 of two kinds having differentrefractive indexes n=1.9 and n=1.5 were employed with being mixed in aratio of 8:2, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.9 and n=1.6 were employed with beingmixed in a ratio of 8:2, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.9 and n=1.8 were employedwith being mixed in a ratio of 8:2, and when only the minute transparentball 12 having a refractive index n=1.9 was employed.

FIG. 44 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.9 and n=1.6 were employed. In FIG. 44, curves 44 a, 44 b, 44c, 44 d, 44 e, 44 f, 44 g and 44 h are luminance curves respectivelyobtained when only the minute transparent ball 12 having a refractiveindex n=1.6 was employed, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.9 and n=1.6 were employedwith being mixed in a ratio of 1:9, when the minute transparent balls 12of two kinds having different refractive indexes n=1.9 and n=1.6 wereemployed with being mixed in a ratio of 3:7, when the minute transparentballs 12 of two kinds having different refractive indexes n=1.9 andn=1.6 were employed with being mixed in a ratio of 5:5, when the minutetransparent balls 12 of two kinds having different refractive indexesn=1.9 and n=1.6 were employed with being mixed in a ratio of 7:3, whenthe minute transparent balls 12 of two kinds having different refractiveindexes n=1.9 and n=1.6 were employed with being mixed in a ratio of8:2, when the minute transparent balls 12 of two kinds having differentrefractive indexes n=1.9 and n=1.6 were employed with being mixed in aratio of 8.5:1.5, and when only the minute transparent ball 12 having arefractive index n=1.9 was employed.

FIG. 45 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.9 and n=1.6 were employed. In FIG. 45, curves 45 a, 45 b, 45c, 45 d, 45 e and 45 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.6 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.9 and n=1.6 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.9 and n=1.6 were employedwith being mixed in a ratio of 6:4, when the minute transparent balls 12of two kinds having different refractive indexes n=1.9 and n=1.6 wereemployed with being mixed in a ratio of 19:1, when the minutetransparent balls 12 of two kinds having different refractive indexesn=1.9 and n=1.6 were employed with being mixed in a ratio of 97:3, andwhen only the minute transparent ball 12 having a refractive index n=1.9was employed.

Study of FIGS. 44 and 45 reveals that the gain curves shown in FIGS. 44and 45 coincides with each other and hence this simulation result shownin FIG. 44 is proper.

Table 2 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.9 and n=1.6 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 2 screen arrangement gain shading gain 30° n = 1.9 n = 1.6 peak30° 20° 2.4 or more 33% or more 100%   0% 1.952 49% 30% X ◯ 98%  2%2.326 41% 41% X ◯ 97%  3% 2.512 38% 45% ◯ ◯ 96%  4% 2.699 35% 49% ◯ ◯95%  5% 2.886 32% 52% ◯ X 80% 20% 5.686 15% 76% ◯ X 60% 40% 9.420  8%85% ◯ X 40% 60% 13.154  5% 89% ◯ X 20% 80% 16.888  3% 92% ◯ X 10% 90%18.755  3% 92% ◯ X  0% 100%  20.622  2% 93% ◯ X

Study of Table 2 reveals that the screen employing the minutetransparent ball 12 of two kinds having the refractive indexes of n=1.9and n=1.6 and mixed in ratios of 97:3 and 96:4 could satisfy theconditions of the peak gain of 2.4 or more and the gain obtained at thebend angle of 30° being equal to or larger than 33%.

FIG. 46 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=2.1 and n=1.9 were employed. In FIG. 46, curves 46 a, 46 b, 46c, 46 d, 46 e and 46 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.9 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=2.1 and n=1.9 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=2.1 and n=1.9 were employedwith being mixed in a ratio of 4:6, when the minute transparent balls 12of two kinds having different refractive indexes n=2.1 and n=1.9 wereemployed with being mixed in a ratio of 6:4, when the minute transparentballs 12 of two kinds having different refractive indexes n=2.1 andn=1.9 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=2.1 wasemployed.

Table 3 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=2.1 And n=1.9 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 3 screen arrangement gain shading gain 30° n = 2.1 n = 1.9 peak30° 20° 2.4 or more 33% or more 100%   0% 1.192 64% 18% X ◯ 90% 10%1.268 62% 20% X ◯ 80% 20% 1.344 60% 21% X ◯ 70% 30% 1.420 58% 23% X ◯60% 40% 1.496 56% 24% X ◯ 50% 50% 1.572 55% 25% X ◯ 40% 60% 1.648 53%26% X ◯ 30% 70% 1.724 52% 27% X ◯ 20% 80% 1.800 51% 28% X ◯ 10% 90%1.876 50% 29% X ◯  0% 100%  1.952 49% 30% X ◯

Study of Table 3 reveals that the screen employing the minutetransparent ball 12 of two kinds having the refractive indexes of n=2.1and n=1.9 couldn't satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

FIG. 47 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=2.1 and n=1.8 were employed. In FIG. 47, curves 47 a, 47 b, 47c, 47 d, 47 e and 47 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.8 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=2.1 and n=1.8 were employed with beingmixed in a ratio of 15:85, when the minute transparent balls 12 of twokinds having different refractive indexes n=2.1 and n=1.8 were employedwith being mixed in a ratio of 2:8, when the minute transparent balls 12of two kinds having different refractive indexes n=2.1 and n=1.8 wereemployed with being mixed in a ratio of 44:56, when the minutetransparent balls 12 of two kinds having different refractive indexesn=2.1 and n=1.8 were employed with being mixed in a ratio of 6:4, andwhen only the minute transparent ball 12 having a refractive index n=2.1was employed.

Table 4 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=2.1 and n=1.8 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 4 screen arrangement gain shading gain 30° n = 2.1 n = 1.8 peak30° 20° 2.4 or more 33% or more 100%   0% 1.192 64% 18% X ◯ 80% 20%1.626 50% 30% X ◯ 60% 40% 2.060 43% 37% X ◯ 45% 55% 2.386 39% 41% X ◯44% 56% 2.408 38% 41% ◯ ◯ 30% 70% 2.712 36% 44% ◯ ◯ 20% 80% 2.929 34%45% ◯ ◯ 16% 84% 3.016 33% 46% ◯ ◯ 15% 85% 3.038 33% 46% ◯ X 10% 90%3.146 33% 47% ◯ X  0% 100%  3.363 31% 48% ◯ X

Study of Table 4 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=2.1and n=1.8 and mixed in a ratio of the former ranging from 16% to 44% andin a corresponding ratio of the latter ranging from 84% to 56% couldsatisfy the conditions of the peak gain of 2.4 or more and the gainobtained at the bend angle of 30° being equal to or larger than 33%.

FIG. 48 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=2.1 and n=1.7 were employed. In FIG. 48, curves 48 a, 48 b, 48c, 48 d, 48 e and 48 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.7 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=2.1 and n=1.7 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=2.1 and n=1.7 were employedwith being mixed in a ratio of 4:6, when the minute transparent balls 12of two kinds having different refractive indexes n=2.1 and n=1.7 wereemployed with being mixed in a ratio of 6:4, when the minute transparentballs 12 of two kinds having different refractive indexes n=2.1 andn=1.7 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=2.1 wasemployed.

Table 5 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=2.1 and n=1.7 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 5 screen arrangement gain shading gain 30° n = 2.1 n = 1.7 peak30° 20° 2.4 or more 33% or more 100%   0% 1.192 64% 18% X ◯ 90% 10%1.736 45% 38% X ◯ 80% 20% 2.281 34% 48% X ◯ 70% 30% 2.825 28% 55% ◯ X60% 40% 3.370 24% 59% ◯ X 50% 50% 3.914 21% 62% ◯ X 40% 60% 4.459 19%65% ◯ X 30% 70% 5.003 17% 67% ◯ X 20% 80% 5.548 15% 68% ◯ X 10% 90%6.092 14% 69% ◯ X  0% 100%  6.637 13% 70% ◯ X

Study of Table 5 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=2.1and n=1.7 couldn't satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

FIG. 49 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=2.1 and n=1.6 were employed. In FIG. 49, curves 49 a, 49 b, 49c, 49 d, 49 e and 49 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.6 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=2.1 and n=1.6 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=2.1 and n=1.6 were employedwith being mixed in a ratio of 4:6, when the minute transparent balls 12of two kinds having different refractive indexes n=2.1 and n=1.6 wereemployed with being mixed in a ratio of 6:4, when the minute transparentballs 12 of two kinds having different refractive indexes n=2.1 andn=1.6 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=2.1 wasemployed.

Table 6 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=2.1 and n=1.6 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 6 screen arrangement gain shading gain 30° n = 2.1 n = 1.6 peak30° 20° 2.4 or more 33% or more 100%   0% 1.192 64%  18% X ◯ 90% 10%3.315 23%  67% ◯ X 80% 20% 5.078 14%  79% ◯ X 70% 30% 7.021 10%  84% ◯ X60% 40% 8.964 7% 87% ◯ X 50% 50% 10.907 6% 89% ◯ X 40% 60% 12.850 4% 90%◯ X 30% 70% 14.793 4% 91% ◯ X 20% 80% 16.736 3% 92% ◯ X 10% 90% 18.6793% 93% ◯ X  0% 100%  20.622 2% 93% ◯ X

Study of Table 6 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=2.1and n=1.6 could not satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

FIG. 50 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=2.1 and n=1.5 were employed. In FIG. 50, curves 50 a, 50 b, 50c, 50 d, 50 e and 50 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.5 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=2.1 and n=1.5 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=2.1 and n=1.5 were employedwith being mixed in a ratio of 4:6, when the minute transparent balls 12of two kinds having different refractive indexes n=2.1 and n=1.5 wereemployed with being mixed in a ratio of 6:4, when the minute transparentballs 12 of two kinds having different refractive indexes n=2.1 andn=1.5 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=2.1 wasemployed.

Table 7 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=2.1 and n=1.5 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 7 screen arrangement gain shading gain 30° n = 2.1 n = 1.5 peak30° 20° 2.4 or more 33% or more 100%   0% 1.192 64%   20% X ◯ 90% 10%40.715 2%  18% ◯ X 80% 20% 80.238 1%  98% ◯ X 70% 30% 119.76 0%  99% ◯ X60% 40% 159.28 0%  99% ◯ X 50% 50% 198.81 0% 100% ◯ X 40% 60% 238.33 0%100% ◯ X 30% 70% 277.85 0% 100% ◯ X 20% 80% 317.38 0% 100% ◯ X 10% 90%356.90 0% 100% ◯ X  0% 100%  396.42 0% 100% ◯ X

Study of Table 7 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=2.1and n=1.5 and mixed in a ratio of the former ranging from 16% to 44% andin a corresponding ratio of the latter ranging from 84% to 56% couldsatisfy the conditions of the peak gain of 2.4 or more and the gainobtained at the bend angle of 30° being equal to or larger than 33%.

FIG. 51 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.9 and n=1.8 were employed. In FIG. 51, curves 51 a, 51 b, 51c, 51 d, 51 e and 51 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.8 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.9 and n=1.8 were employed with beingmixed in a ratio of 17:83, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.9 and n=1.8 were employedwith being mixed in a ratio of 2:8, when the minute transparent balls 12of two kinds having different refractive indexes n=1.9 and n=1.8 wereemployed with being mixed in a ratio of 5:5, when the minute transparentballs 12 of two kinds having different refractive indexes n=1.9 andn=1.8 were employed with being mixed in a ratio of 69:31, and when onlythe minute transparent ball 12 having a refractive index n=1.9 wasemployed.

Table 8 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.9 and n=1.8 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 8 screen arrangement gain shading gain 30° n = 1.9 n = 1.8 peak30° 20° 2.4 or more 33% or more 100%   0% 1.952 49% 30% X ◯ 80% 20%2.235 44% 35% X ◯ 69% 31% 2.390 41% 38% X ◯ 68% 32% 2.404 41% 38% ◯ ◯50% 50% 2.658 38% 41% ◯ ◯ 30% 70% 2.940 35% 44% ◯ ◯ 20% 80% 3.081 34%45% ◯ ◯ 18% 82% 3.109 33% 46% ◯ ◯ 17% 83% 3.123 33% 46% ◯ X 10% 90%3.222 32% 47% ◯ X  0% 100%  3.363 31% 48% ◯ X

Study of Table 8 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.9and n=1.8 and mixed in a ratio of the former ranging from 18% to 68% andin a corresponding ratio of the latter ranging from 82% to 32% couldsatisfy the conditions of the peak gain of 2.4 or more and the gainobtained at the bend angle of 30° being equal to or larger than 33%.

FIG. 52 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.9 and n=1.7 were employed. In FIG. 52, curves 52 a, 52 b, 52c, 52 d, 52 e and 52 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.7 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.9 and n=1.7 were employed with beingmixed in a ratio of 3:7, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.9 and n=1.7 were employedwith being mixed in a ratio of 7:3, when the minute transparent balls 12of two kinds having different refractive indexes n=1.9 and n=1.7 wereemployed with being mixed in a ratio of 82:18, when the minutetransparent balls 12 of two kinds having different refractive indexesn=1.9 and n=1.7 were employed with being mixed in a ratio of 9:1, andwhen only the minute transparent ball 12 having a refractive index n=1.9was employed.

Table 9 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.9 and n=1.7 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 9 screen arrangement gain shading gain 30° n = 1.9 n = 1.7 peak30° 20° 2.4 or more 33% or more 100%   0% 1.952 49% 30% X ◯ 91%  9%2.374 40% 40% X ◯ 90% 10% 2.421 39% 41% ◯ ◯ 85% 15% 2.655 36% 45% ◯ ◯82% 18% 2.796 34% 47% ◯ ◯ 81% 19% 2.842 33% 48% ◯ X 70% 30% 3.358 28%54% ◯ X 50% 50% 4.295 21% 61% ◯ X 30% 70% 5.232 17% 66% ◯ X 10% 90%6.168 14% 69% ◯ X  0% 100%  6.637 13% 70% ◯ X

Study of Table 9 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.9and n=1.7 and mixed in a ratio of the former ranging from 82% to 90% andin a corresponding ratio of the latter ranging from 18% to 10% couldsatisfy the conditions of the peak gain of 2.4 or more and the gainobtained at the bend angle of 30° being equal to or larger than 33%.

FIG. 53 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.9 and n=1.6 were employed. In FIG. 53, curves 53 a, 53 b, 53c, 53 d, 53 e and 53 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.6 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.9 and n=1.6 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.9 and n=1.6 were employedwith being mixed in a ratio of 6:4, when the minute transparent balls 12of two kinds having different refractive indexes n=1.9 and n=1.6 wereemployed with being mixed in a ratio of 95:5, when the minutetransparent balls 12 of two kinds having different refractive indexesn=1.9 and n=1.6 were employed with being mixed in a ratio of 97:3, andwhen only the minute transparent ball 12 having a refractive index n=1.9was employed.

Table 10 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.9 and n=1.6 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 10 screen arrangement gain shading gain 30° n = 1.9 n = 1.6 peak30° 20° 2.4 or more 33% or more 100%   0% 1.952 49% 30% X ◯ 98%  2%2.326 41% 41% X ◯ 97%  3% 2.512 38% 45% ◯ ◯ 96%  4% 2.699 35% 49% ◯ ◯95%  5% 2.886 32% 52% ◯ X 80% 20% 5.686 15% 76% ◯ X 60% 40% 9.420  8%85% ◯ X 40% 60% 13.154  5% 89% ◯ X 20% 80% 16.888  3% 92% ◯ X 10% 90%18.755  3% 92% ◯ X  0% 100%  20.622  2% 93% ◯ X

Study of Table 10 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.9and n=1.6 and mixed in a ratio of the former ranging from 96% to 97% andin a corresponding ratio of the latter ranging from 4% to 3% couldsatisfy the conditions of the peak gain of 2.4 or more and the gainobtained at the bend angle of 30° being equal to or larger than 33%.

FIG. 54 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.9 and n=1.5 were employed. In FIG. 54, curves 54 a, 54 b, 54c, 54 d, 54 e and 54 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.5 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.9 and n=1.5 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.9 and n=1.5 were employedwith being mixed in a ratio of 6:4, when the minute transparent balls 12of two kinds having different refractive indexes n=1.9 and n=1.5 wereemployed with being mixed in a ratio of 4:6, when the minute transparentballs 12 of two kinds having different refractive indexes n=1.9 andn=1.5 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=1.9 wasemployed.

Table 11 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.9 and n=1.5 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 11 screen gain arrangement gain shading 2.4 or 30° n = 1.9 n = 1.5peak 30° 20° more 33% or more 100%   0% 1.952 49%  30% X ◯ 90% 10%41.399  2.1%  97% ◯ X 80% 20% 80.846  1.0%  99% ◯ X 70% 30% 120.29  0.6% 99% ◯ X 60% 40% 159.74  0.4%  99% ◯ 50% 50% 199.19  0.2% 100% ◯ X 40%60% 238.63  0.2% 100% ◯ X 30% 70% 278.08  0.1% 100% ◯ X 20% 80% 317.53 0.1% 100% ◯ X 10% 90% 356.98  0% 100% ◯ X  0% 100%  396.42  0% 100% ◯ X

Study of Table 11 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.9and n=1.5 could not satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

FIG. 55 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.8 and n=1.7 were employed. In FIG. 55, curves 55 a, 55 b, 55c, 55 d, 55 e and 55 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.7 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.8 and n=1.7 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.8 and n=1.7 were employedwith being mixed in a ratio of 6:4, when the minute transparent balls 12of two kinds having different refractive indexes n=1.8 and n=1.7 wereemployed with being mixed in a ratio of 4:6, when the minute transparentballs 12 of two kinds having different refractive indexes n=1.8 andn=1.7 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=1.8 wasemployed.

Table 12 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.8 and n=1.7 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 12 screen arrangement gain shading gain 30° n = 1.8 n = 1.7 peak30° 20° 2.4 or more 33% or more 100%   0% 3.363 31% 48% ◯ X 90% 10%3.691 28% 52% ◯ X 80% 20% 4.018 25% 55% ◯ X 70% 30% 4.354 23% 58% ◯ X60% 40% 4.673 21% 61% ◯ X 50% 50% 5.000 19% 63% ◯ X 40% 60% 5.327 18%65% ◯ X 30% 70% 5.655 16% 66% ◯ X 20% 80% 5.982 15% 68% ◯ X 10% 90%6.310 14% 69% ◯ X  0% 100%  6.637 13% 70% ◯ X

Study of Table 12 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.8and n=1.7 could not satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

FIG. 56 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.8 and n=1.6 were employed. In FIG. 56, curves 56 a, 56 b, 56c, 56 d, 56 e and 56 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.6 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.8 and n=1.6 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.8 and n=1.6 were employedwith being mixed in a ratio of 6:4, when the minute transparent balls 12of two kinds having different refractive indexes n=1.8 and n=1.6 wereemployed with being mixed in a ratio of 4:6, when the minute transparentballs 12 of two kinds having different refractive indexes n=1.8 andn=1.6 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=1.8 wasemployed.

Table 13 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.8 and n=1.6 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 13 screen arrangement gain shading gain 30° n = 1.8 n = 1.6 peak30° 20° 2.4 or more 33% or more 100%   0% 3.363 31%  48% ◯ X 90% 10%5.089 20%  66% ◯ X 80% 20% 6.815 14%  75% ◯ X 70% 30% 8.541 10%  81% ◯ X60% 40% 10.267 8% 84% ◯ X 50% 50% 11.993 6% 87% ◯ X 40% 60% 13.718 5%89% ◯ X 30% 70% 15.444 4% 90% ◯ X 20% 80% 17.170 3% 91% ◯ X 10% 90%18.896 3% 92% ◯ X  0% 100%  20.622 2% 93% ◯ X

Study of Table 13 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.8and n=1.6 could not satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

FIG. 57 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.8 and n=1.5 were employed. In FIG. 57, curves 57 a, 57 b, 57c, 57 d, 57 e and 57 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.5 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.8 and n=1.5 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.8 and n=1.5 were employedwith being mixed in a ratio of 6:4, when the minute transparent balls 12of two kinds having different refractive indexes n=1.8 and n=1.5 wereemployed with being mixed in a ratio of 4:6, when the minute transparentballs 12 of two kinds having different refractive indexes n=1.8 andn=1.5 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=1.8 wasemployed.

Table 14 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.8 and n=1.5 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 14 screen arrangement gain shading gain 30° n = 1.8 n = 1.5 peak30° 20° 2.4 or more 33% or more 100%   0% 3.363 31%   48% ◯ X 90% 10%42.669 2%  96% ◯ X 80% 20% 81.975 1%  98% ◯ X 70% 30% 121.28 1%  99% ◯ X60% 40% 160.59 0%  99% ◯ X 50% 50% 199.89 0% 100% ◯ X 40% 60% 239.20 0%100% ◯ X 30% 70% 278.50 0% 100% ◯ X 20% 80% 317.81 0% 100% ◯ X 10% 90%357.12 0% 100% ◯ X  0% 100%  396.42 0% 100% ◯ X

Study of Table 14 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.8and n=1.5 could not satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

FIG. 58 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.7 and n=1.6 were employed. In FIG. 58, curves 58 a, 58 b, 58c, 58 d, 58 e and 58 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.6 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.7 and n=1.6 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.7 and n=1.6 were employedwith being mixed in a ratio of 6:4, when the minute transparent balls 12of two kinds having different refractive indexes n=1.7 and n=1.6 wereemployed with being mixed in a ratio of 4:6, when the minute transparentballs 12 of two kinds having different refractive indexes n=1.7 andn=1.6 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=1.7 wasemployed.

Table 15 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.7 and n=1.6 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 15 screen arrangement gain shading gain 30° n = 1.7 n = 1.6 peak30° 20° 2.4 or more 33% or more 100%   0% 6.637 13%  70% ◯ X 90% 10%8.035 10%  76% ◯ X 80% 20% 9.434 8% 80% ◯ X 70% 30% 10.832 7% 83% ◯ X60% 40% 12.231 6% 86% ◯ X 50% 50% 13.629 5% 88% ◯ X 40% 60% 15.028 4%89% ◯ X 30% 70% 16.426 4% 90% ◯ X 20% 80% 17.825 3% 91% ◯ X 10% 90%19.223 3% 92% ◯ X  0% 100%  20.622 2% 93% ◯ X

Study of Table 15 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.7and n=1.6 could not satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

FIG. 59 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.7 and n=1.5 were employed. In FIG. 59, curves 59 a, 59 b, 59c, 59 d, 59 e and 59 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.5 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.7 and n=1.5 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.7 and n=1.5 were employedwith being mixed in a ratio of 6:4, when the minute transparent balls 12of two kinds having different refractive indexes n=1.7 and n=1.5 wereemployed with being mixed in a ratio of 4:6, when the minute transparentballs 12 of two kinds having different refractive indexes n=1.7 andn=1.5 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=1.7 wasemployed.

Table 16 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.7 and n=1.5 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 16 screen arrangement gain shading gain 30° n = 1.7 n = 1.5 peak30° 20° 2.4 or more 33% or more 100%   0% 6.637 13% 70% ◯ X 90% 10%45.615 2%  96% ◯ X 80% 20% 84.594 1%  98% ◯ X 70% 30% 123.57 0%  99% ◯ X60% 40% 162.55 0%  99% ◯ X 50% 50% 201.53 0% 100% ◯ X 40% 60% 240.51 0%100% ◯ X 30% 70% 279.49 0% 100% ◯ X 20% 80% 318.47 0% 100% ◯ X 10% 90%357.44 0% 100% ◯ X  0% 100%  396.42 0% 100% ◯ X

Study of Table 16 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.7and n=1.5 could not satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

FIG. 60 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of two kinds having different refractiveindexes n=1.6 and n=1.5 were employed. In FIG. 60, curves 60 a, 60 b, 60c, 60 d, 60 e and 60 f are luminance curves respectively obtained whenonly the minute transparent ball 12 having a refractive index n=1.5 wasemployed, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.6 and n=1.5 were employed with beingmixed in a ratio of 2:8, when the minute transparent balls 12 of twokinds having different refractive indexes n=1.6 and n=1.5 were employedwith being mixed in a ratio of 6:4, when the minute transparent balls 12of two kinds having different refractive indexes n=1.6 and n=1.5 wereemployed with being mixed in a ratio of 4:6, when the minute transparentballs 12 of two kinds having different refractive indexes n=1.6 andn=1.5 were employed with being mixed in a ratio of 8:2, and when onlythe minute transparent ball 12 having a refractive index n=1.6 wasemployed.

Table 17 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of two kinds havingthe refractive indexes of n=1.6 and n=1.5 were employed. In this case,when a value of the peak gain is equal to or larger than 2.4, the resultis evaluated with an open circle, and when the value is smaller than2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 17 screen arrangement gain shading gain 30° n = 1.6 n = 1.5 peak30° 20° 2.4 or more 33% or more 100%   0% 20.622 2%  93% ◯ X 90% 10%58.202 1%  98% ◯ X 80% 20% 95.782 0%  99% ◯ X 70% 30% 133.36 0%  99% ◯ X60% 40% 170.94 0%  99% ◯ X 50% 50% 208.52 0% 100% ◯ X 40% 60% 246.10 0%100% ◯ X 30% 70% 283.68 0% 100% ◯ X 20% 80% 321.26 0% 100% ◯ X 10% 90%358.84 0% 100% ◯ X  0% 100%  396.42 0% 100% ◯ X

Study of Table 17 reveals that the screen employing the minutetransparent balls 12 of two kinds having the refractive indexes of n=1.6and n=1.5 could not satisfy the conditions of the peak gain of 2.4 ormore and the gain obtained at the bend angle of 30° being equal to orlarger than 33%.

The results shown in FIGS. 41 to 60 and Tables 1 to 17 are summarized inTable 18.

TABLE 18 refrac- ratio of ball having refractive index to the tive wholeindex 2.1 1.9 1.8 1.7 1.6 1.5 2.1 X X 56 to 84 X X X 1.9 X X 32 to 82 10to 18 3 to 4 X 1.8 16 to 44 18 to 68 X X X X 1.7 X 82 to 90 X X X X 1.6X 96 to 97 X X X X 1.5 X X X X X X

Table 18 shows the results obtained when two kinds of the minutetransparent balls having the refractive indexes of 1.5, 1.6, 1.7, 1.8,1.9 and 2.1 were optionally mixed to form the screen and luminance ofthe screen was measured. Table 18 shows ratios (%) of the minutetransparent balls to be mixed to the whole minute transparent balls inthe combinations of the minute transparent balls of two kinds whichsatisfy the conditions of the peak gain of 2.4 or more and the gainobtained at the bend angle of 30° being equal to or larger than 33%.

Study of Table 18 reveals that when two kinds of the minute transparentballs having the refractive indexes of 1.5, 1.6, 1.7, 1.8, 1.9 and 2.1were optionally mixed in a predetermined ratio to form the screen, thescreen having an excellent gain obtained at the bend angle of 30° can beachieved.

The present invention is not limited to the combinations of two kinds ofthe minute transparent balls having different refractive indexes.According to the present invention, even if three kinds of the minutetransparent balls having different refractive indexes are mixed, it ispossible to realize the excellent plano lens and the excellentrear-projection type projector screen.

FIG. 61 is a graph showing measurement of luminance obtained when theminute transparent balls 12 of three kinds having different refractiveindexes n=1.7, n=1.8 and n=1.9 were employed.

In FIG. 61, curves 61 a, 61 b, 61 c, 61 d, and 61 e are luminance curvesrespectively obtained when the minute transparent balls 12 of two kindshaving different refractive indexes n=1.9, n=1.8 and n=1.7 were employedwith being mixed in a ratio of 20:75:5, when the minute transparentballs 12 of three kinds having different refractive indexes n=1.9, n=1.8and n=1.7 were employed with being mixed in a ratio of 30:30:40, whenthe minute transparent balls of three kinds having different refractiveindexes n=1.9, n=1.8 and n=1.7 were employed with being mixed in a ratioof 60:35:5, when the minute transparent balls 12 of two kinds havingdifferent refractive indexes n=1.9, n=1.8 and n=1.7 were employed withbeing mixed in a ratio of 70:20:10, and when the minute transparentballs 12 of three kinds having different refractive indexes n=1.9, n=1.8and n=1.7 were employed with being mixed in a ratio of 90:5:5.

Table 19 shows a simulation result of a peak gain of a screen, a gainobtained at a bend angle of 30° and shading obtained at a bend angle of20° obtained when the minute transparent balls 12 of three kinds havingthe refractive indexes of n=1.9, n=1.8 and n=1.7 were employed. In thiscase, when a value of the peak gain is equal to or larger than 2.4, theresult is evaluated with an open circle, and when the value is smallerthan 2.4, the result is evaluated with a cross. When a value of the gainobtained at a bend angle of 30° is equal to or larger than ⅓ of larger,i.e., 33% or larger of the peak gain, the result is evaluated with anopen circle, and when the value is smaller than 33%, the result isevaluated with a cross

TABLE 19 screen gain 30° arrangement gain shading 2.4 or 33% or n = 1.9n = 1.8 n = 1.7 peak 30° 20° more more 90%  5%  5% 2.2571 43% 37% X ◯70% 20% 10% 2.703  36% 44% ◯ ◯ 60% 35%  5% 2.6804 37% 44% ◯ ◯ 30% 30%40% 4.2494 22% 59% ◯ X 20% 75%  5% 3.2448 32% 48% ◯ X

Study of Table 19 reveals that the screen employing the minutetransparent balls 12 of three kinds having the refractive indexes ofn=1.9, n=1.8 and n=1.7 in a ratio of 2:35:60 to 10:20:70 could satisfythe conditions of the peak gain of 2.4 or more and the gain obtained atthe bend angle of 30° being equal to or larger than 33%.

While in the above embodiments the refractive index of the minutetransparent balls 12 is changed to amend the amount of the lighttransmitted through the lens 10 or the screen 10S, absorbance orspectral absorbance of at least one or more of the transparent basemember 11 or 41 and the base member 31 is gradually or stepwise changed.Simultaneously with the above arrangement, or instead of the abovearrangement, absorbance or spectral absorbance of at least one layer ofthe transparent layers 15, 25, 26 or the like is gradually or stepwisechanged, thereby the emission light being made substantially even orbeing positively distributed in a desired distribution pattern.

In the rear-projection type video display apparatus employing the screenaccording to the present invention, the projected picture can becontinuously or intermittently enlarged or reduced by providing azooming mechanism in the optical system of the video projector unit 1 orby changing a distance between the screen and the video projector unit1. While in the conventional screen employing the lenticular lens theoptical system and the distance between the screen and the videoprojector unit are set in a constant state defined by a design becauseof moire, when the arrangement according to the present invention isemployed, the present invention is based on the dense arrangement of theminute transparent balls and hence the resolution is improved, therebysuch arrangement being realized.

In the rear-projection type video display apparatus employing the screenaccording to the present invention, when the center illuminance on thevideo projection side of light for the screen is set to 500 [lux] orhigher. In this case, the center illuminance becomes 200 [cd/m] orlarger which is sufficient in practical use. As a result, a center angleof a conic region where a luminance of 50% of the center illuminance canbe obtained at the viewer side is 45 or greater.

A method of manufacturing the screen, i.e., the plano lens according tothe present invention will be described. When the arrangement shown inFIG. 9 is employed as a basic arrangement and the plane lens or thescreen is formed, i.e., coated by using the basic arrangement, thecolored layer 13 having the adhesion or cohesion which allows the minutetransparent balls to be fixed thereon is deposited on the similarsheet-like or rigid base member. The minute transparent elements aredensely filled on the colored layer, thereby theminute-transparent-layer being formed.

When the arrangement shown in FIG. 10 is employed as a basic arrangementand the plane lens or the screen is formed, i.e., coated by using thebasic arrangement, the transparent layer 15 having adhesion or cohesionwhich allows the minute transparent balls to be fixed thereof isdeposited, i.e., coated on the similar base member 11 and the coloredlayer having adhesion or cohesion which allows the minute transparentballs to be fixed thereon is deposited on the similar base member. Theminute transparent elements are densely filled on the colored layer,thereby the minute-transparent-layer being formed.

The colored layer 13 can be formed by using a colored coating materialcolored with a desired color as the coating material. However, in thecoating, the colorless or white coating material having adhesion orcohesion is used and then colored after being coated.

The process of filling the minute transparent balls 12 in theminute-transparent-ball disposing layers 14 can be carried out byburying type minute transparent balls 12 in the colored layer 13 havingthe adhesion or the cohesion or the colored layer 13 and the transparentlayer 15 by a desired depth so that the minute transparent balls 12should be in contact with or close to each other in a single grainlayer.

When the minute transparent ball disposing layer 14 is formed, anapparatus and a method proposed by the same assignee of the applicationin Japanese patent application No. 7-344488 “minute ball arrangingapparatus and minute ball arranging method” can be applied.Specifically, a supply nozzle for supplying the minute transparent ballsto be finally used in the minute-transparent-ball disposing layer isprepared and the minute transparent balls 12 of an amount which is morethan those finally disposed in the minute-transparent-ball disposinglayer 14 are supplied to the colored layer 13 having the cohesion, thetransparent layer 15 having the cohesion and the transparent layer 26having cohesion. Then, the minute transparent balls 12 are squeezed tobe densely arranged on the entire minute-transparent-ball disposinglayer 14. Moreover, a pressing roller is rotated with a predeterminedpressure thereon, thereby the minute transparent balls 12 being buriedat the light emission side in the colored layer 13, the transparentlayer 15, or the transparent layer 26 or the colored layer 13 and thetransparent layer 15 located thereunder. The vacuum absorber apparatusis brought on the surface side, thereby absorbing and removing theremaining minute transparent balls and the minute transparent ballswhich are not fixed tightly and whose buried amount does not reach apredetermined value. Thus, it is possible to form a desiredminute-transparent-ball disposing layer 14 where only a minutetransparent balls buried in the colored layer 13 or the transparentlayer 15 or the transparent layer 26 by a desired depth are disposed.

In some case, when the plano lens 10 shown in FIG. 10 is manufactured,the colored layer 13 having adhesion or cohesion is formed on thetransparent base member 11. The following method can be employed. Thetransparent layer 15 having the adhesion or cohesion is coated on atransfer sheet (not shown). The minute transparent balls 12 are denselyfilled and arranged in the transparent layer 15 by the above method. Thetransfer sheet is pressed to the colored layer 13 on the transparentbase member 11 with its side having the minute transparent balls 12disposed thereon being opposed thereto, and further pressed so that theminute transparent balls 12 should substantially reach the transparentbase member under the colored layer. In this state, the minutetransparent balls are peeled off from the transfer sheet together withthe transparent layer, thereby being transferred to the transfer basemember side. Thus, the plano lens or the screen on which theminute-transparent-ball disposing layer 14 is formed on the transparentbase member 11 can be manufactured.

When the plano lenses or the screens shown in FIGS>11 and 12 aremanufactured, the transparent protective layer 25 are coated by theabove coating method on the minute-transparent-ball disposing layers 14shown in FIG. 9 and 11 formed by the above method.

In the plano lenses 10 or the screen 10S shown in FIGS. 9 to 12, thetransparent base members 11 are disposed on the light emission sides. Asshown in FIGS. 13 and 14, when the transparent base member 11 isdisposed on the light incidence side, the following method can beemployed. The colored layer having adhesion or cohesion is coated or thetransparent layer 26 having adhesion or cohesion formed on the coloredlayer 13 is coated on a transfer sheet (not shown). The transparentlayer 15 having adhesion or cohesion is similarly coated on the coloredlayer 13. The minute transparent balls 12 are densely buried in thecolored layer 13 or both of the colored layer 13 and the transparentlayer 15 formed thereunder by the above burying method. The transfersheet is pressed to the colored layer 13 on the transparent base member11 with its side having the minute transparent balls 12 disposed thereonbeing opposed thereto, and further pressed so that the minutetransparent balls 12 should substantially reach the transparent basemember under the colored layer. In this state, the minute transparentballs are peeled off from the transfer sheet together with thetransparent layer, thereby being transferred to the transfer base memberside. Thus, the plano lens or the screen on which theminute-transparent-ball disposing layer 14 is formed on the transparentbase member 11 can be manufactured.

Moreover, when the plano lenses 10 or the screens 10S shown in FIGS. 15and 16 are manufactured, the methods of manufacturing the plano lensesor the screens shown in FIGS. 9 to 14 can be applied. Then, theprotective transparent base members 41 formed of the sheet-like andrigid substrates are bonded to the plano lenses or the screens throughthe adhesion layers or by utilizing the adhesion or cohesion of thetransparent layers 26, 15 on the opposite sides thereof relative to thetransparent base members 11.

FIG. 62 shows an embodiment of a minute-transparent-ball 12 a havingconvex projections 32 distributed over its surface, and FIG. 63 shows anembodiment of a minute-transparent ball 12 b having convex depressions33 distributed over its surface.

Use of the plano lens, the rear-projection type projector screen and therear-projection type video display apparatus according to the presentinvention can solve the above problems of the lenticular lens.

Specifically, according to the present invention, since the externallight is effectively prevented from travelling in undesired directions,it is possible to improve the contrast of the picture.

Since it is unnecessary to provide the smoke plate or the like, it ispossible to prevent the luminance from being lowered. As a result, it ispossible to avoid use of the light source consuming a large power, andhence it is possible to reduce a consumed power, to reduce a generatedheat, and to prevent the costs from being increased.

According to the present invention, since the light can be widelydiffused in both of the vertical and horizontal directions, the range inwhich the user can observe a sharp picture is extended, and it ispossible to avoid a partial unevenness of luminance.

The piano lens according to the present invention can be easilymanufactured and handled as compared with the lenticular lens, whichprevents the costs from being increased.

According to the plano lens of the present invention, the resolution isimproved as compared with that obtained when the lenticular lens isused.

It is possible to easily amend the illumination distribution to therebyachieve a desired luminance distribution.

When both of the Fresnel lens and the lenticular lens are used, it ispossible to above multiple reflections therebetween.

Moreover, since the moire hardly occurs in the plano lens according tothe present invention, restriction of the design in the rear-projectiontype projector is relaxed. It is possible to easily equip a zoomingmechanism or the like thereon.

According to the present invention, since the minute transparent ballshaving different refractive indexes are mixed in a preferable ratio, itis possible to form the screen having a high peak gain and having acomparatively high gain even at a bend angle of 30°.

The glass minute transparent balls having the refractive indexes of 1.5,1.6, 1.7, 1.8, 1.9 and 2.1 can be manufactured. The glass minutetransparent balls having the refractive indexes of 1.5, 1.9 and 2.1 aremass-produced, and hence generally available with low costs. On theother hand, The glass minute transparent balls having the refractiveindexes of 1.6, 1.7 and 1.8 are comparatively expensive. According tothe present invention, since the inexpensive minute transparent balls oftwo kinds or more are mixed to form the screen or since only a smallamount of the expensive minute transparent balls are used for optionalmixing thereof to form the screen, it is possible to the screen formingthe rear-projection type video display apparatus obtaining an excellentgain curve with an inexpensive cost.

Having described preferred embodiments of the present invention withreference to the accompanying drawings, it is to be understood that thepresent invention is not limited to the above-mentioned embodiments andthat various changes and modifications can be effected therein by oneskilled in the art without departing from the spirit or scope of thepresent invention as defined in the appended claims.

What is claimed is:
 1. A piano lens comprising: a transparent basemember having a light incident side and a light emission side; aplurality of minute transparent balls disposed two-dimensionally in asingle ball layer on said transparent base member with said minutetransparent balls being substantially adjacent each other; a coloredlayer on said transparent base member with said minute transparent ballsrespectively partially buried in said colored layer so that each of saidminute transparent balls has an exposed surface portion projecting fromsaid colored layer toward said light incident side; and each of saidminute transparent balls having an optical characteristic selected fromthe group consisting of absorbence, spectral absorbence and refractiveindex, and the optical characteristic of some of said minute transparentballs differing in value from others of said minute transparent balls,and said minute transparent balls being respectively disposed in saidsingle ball layer with a non-uniform two-dimensional distribution ofsaid differing values of said optical characteristic.
 2. The piano lensas claimed in claim 1, further comprising a transparent layer disposedbetween said minute transparent balls and said transparent base member.3. The piano lens as claimed in claim 1 further comprising a protectivetransparent layer formed on said minute transparent balls at a side ofsaid minute transparent balls opposite to said transparent layer.
 4. Thepiano lens as claimed in claim 1 further comprising a protectivetransparent base member layer on said transparent base member at a sideof said transparent base member opposite said minute transparent balls.5. The piano lens as claimed in claim 1 further comprising a Fresnellens bonded to said light incident side of said base member.
 6. Thepiano lens as claimed in claim 1 further comprising an anti-reflectionlayer disposed at said light incident side of said base member.
 7. Thepiano lens as claimed in claim 1 further comprising an anti-reflectionlayer disposed at said light emission side of said base member.
 8. Thepiano lens as claimed in claim 1 further comprising a firstanti-reflection layer formed on said light incident side of said basemember and a second anti-reflection layer formed on said light emissionside of said base member.
 9. The piano lens as claimed in claim 1further comprising a protective layer disposed at said light incidentside of said base member.
 10. The piano lens as claimed in claim 1further comprising a protective layer disposed at said light emissionside of said base member.
 11. The piano lens as claimed in claim 1further comprising a first protective layer formed on said lightincident side of said base member and a second protective layer formedon said light emission side of said base member.
 12. The piano lens asclaimed in claim 1 wherein each of said minute transparent balls has adiameter, and wherein each of said minute transparent balls projectsfrom said colored layer by an amount which is 30% or more of saiddiameter, and wherein said colored layer has a thickness which is lessthan 70% of said diameter.
 13. The piano lens as claimed in claim 1wherein said colored layer has an absorbence characteristic selectedfrom the group consisting of absorbence and spectral absorbence andwherein said transparent base member has an absorbence characteristicselected from the group consisting of absorbence and spectralabsorbence, and wherein said absorbence characteristic of said coloredlayer differs in value from said absorbence characteristic of saidtransparent base member.
 14. The piano lens as claimed in claim 1wherein each of said minute transparent balls has a diameter which isless than 100 μm.
 15. The piano lens as claimed in claim 1 wherein eachof said minute transparent balls has a diameter, and wherein said minutetransparent balls collectively exhibit an average diameter, and whereinno one of said minute transparent balls has a diameter which differsfrom said average diameter by more than 10% of said average diameter.16. The piano lens as claimed in claim 1 wherein said transparent basemember is disposed at said light incident side of said base member andhas a refractive index, and wherein each of said minute transparentballs has a refractive index which is larger than said refractive indexof said transparent base member.
 17. The piano lens as claimed in claim16 wherein each of said minute transparent balls has a refractive indexwhich is greater than or equal to 1.4.
 18. The piano lens as claimed inclaim 1 wherein said optical characteristic is the refractive index andwherein said plano lens has a peak gain which is greater than or equalto 2.4, and a gain at a bend angle of 30° which is greater than or equalto ⅓ of said peak gain.
 19. The piano lens as claimed in claim 1 whereinsaid base member has a center and a periphery, and wherein said minutetransparent balls are distributed in said single ball layer so that saidoptical characteristic changes gradually from minute transparent ballsdisposed at said center of said base member to minute transparent ballsdistributed at said periphery of said base member.
 20. The piano lens asclaimed in claim 1 wherein said base member has a center and aperiphery, and wherein said minute transparent balls are distributed insaid single ball layer so that said optical characteristic changes insteps from minute transparent balls disposed at said center of said basemember to minute transparent balls distributed at said periphery of saidbase member.
 21. The piano lens as claimed in claim 1 wherein at leastsome of said minute transparent balls have a plurality of convexprojections on a surface thereof.
 22. The piano lens as claimed in claim1 wherein at least some of said minute transparent balls have aplurality of concave depressions on a surface thereof.